Regularity for Lorentz Metrics under Curvature Bounds

Let (M, g) be an (n+1) dimensional space-time, with bounded curvature with respect to a bounded framing. If (M, g) is vacuum or satisfies a mild condition on the stress-energy tensor, then we show that (M, g) locally admits coordinate systems in which the Lorentz metric is well-controlled in the (space-time) Sobolev space L^{2,p}, for any finite p.Comment: 18p

Mode spectrum and temporal soliton formation in optical microresonators

The formation of temporal dissipative solitons in optical microresonators enables compact, high repetition rate sources of ultra-short pulses as well as low noise, broadband optical frequency combs with smooth spectral envelopes. Here we study the influence of the resonator mode spectrum on temporal soliton formation. Using frequency comb assisted diode laser spectroscopy, the measured mode structure of crystalline MgF2 resonators are correlated with temporal soliton formation. While an overal general anomalous dispersion is required, it is found that higher order dispersion can be tolerated as long as it does not dominate the resonator's mode structure. Mode coupling induced avoided crossings in the resonator mode spectrum are found to prevent soliton formation, when affecting resonator modes close to the pump laser. The experimental observations are in excellent agreement with numerical simulations based on the nonlinear coupled mode equations, which reveal the rich interplay of mode crossings and soliton formation

Heat transfer and Fourier's law in off-equilibrium systems

We study the most suitable procedure to measure the effective temperature in off-equilibrium systems. We analyze the stationary current established between an off-equilibrium system and a thermometer and the necessary conditions for that current to vanish. We find that the thermometer must have a short characteristic time-scale compared to the typical decorrelation time of the glassy system to correctly measure the effective temperature. This general conclusion is confirmed analyzing an ensemble of harmonic oscillators with Monte Carlo dynamics as an illustrative example of a solvable model of a glass. We also find that the current defined allows to extend Fourier's law to the off-equilibrium regime by consistently defining effective transport coefficients. Our results for the oscillator model explain why thermal conductivities between thermalized and frozen degrees of freedom in structural glasses are extremely small.Comment: 7 pages, REVTeX, 4 eps figure

Temporal solitons in optical microresonators

Dissipative solitons can emerge in a wide variety of dissipative nonlinear systems throughout the fields of optics, medicine or biology. Dissipative solitons can also exist in Kerr-nonlinear optical resonators and rely on the double balance between parametric gain and resonator loss on the one hand and nonlinearity and diffraction or dispersion on the other hand. Mathematically these solitons are solution to the Lugiato-Lefever equation and exist on top of a continuous wave (cw) background. Here we report the observation of temporal dissipative solitons in a high-Q optical microresonator. The solitons are spontaneously generated when the pump laser is tuned through the effective zero detuning point of a high-Q resonance, leading to an effective red-detuned pumping. Red-detuned pumping marks a fundamentally new operating regime in nonlinear microresonators. While usually unstablethis regime acquires unique stability in the presence of solitons without any active feedback on the system. The number of solitons in the resonator can be controlled via the pump laser detuning and transitions to and between soliton states are associated with discontinuous steps in the resonator transmission. Beyond enabling to study soliton physics such as soliton crystals our observations open the route towards compact, high repetition-rate femto-second sources, where the operating wavelength is not bound to the availability of broadband laser gain media. The single soliton states correspond in the frequency domain to low-noise optical frequency combs with smooth spectral envelopes, critical to applications in broadband spectroscopy, telecommunications, astronomy and low phase-noise microwave generation.Comment: Includes Supplementary Informatio

Extrapolation of K to \pi\pi decay amplitude

We examine the uncertainties involved in the off-mass-shell extrapolation of the $K\rightarrow \pi\pi$ decay amplitude with emphasis on those aspects that have so far been overlooked or ignored. Among them are initial-state interactions, choice of the extrapolated kaon field, and the relation between the asymptotic behavior and the zeros of the decay amplitude. In the inelastic region the phase of the decay amplitude cannot be determined by strong interaction alone and even its asymptotic value cannot be deduced from experiment. More a fundamental issue is intrinsic nonuniqueness of off-shell values of hadronic matrix elements in general. Though we are hampered with complexity of intermediate-energy meson interactions, we attempt to obtain a quantitative idea of the uncertainties due to the inelastic region and find that they can be much larger than more optimistic views portray.Comment: 16 pages with 5 eps figures in REVTE

The G protein-gated potassium current I(K,ACh) is constitutively active in patients with chronic atrial fibrillation

Background— The molecular mechanism of increased background inward rectifier current (IK1) in atrial fibrillation (AF) is not fully understood. We tested whether constitutively active acetylcholine (ACh)-activated IK,ACh contributes to enhanced basal conductance in chronic AF (cAF). Methods and Results— Whole-cell and single-channel currents were measured with standard voltage-clamp techniques in atrial myocytes from patients with sinus rhythm (SR) and cAF. The selective IK,ACh blocker tertiapin was used for inhibition of IK,ACh. Whole-cell basal current was larger in cAF than in SR, whereas carbachol (CCh)-activated IK,ACh was lower in cAF than in SR. Tertiapin (0.1 to 100 nmol/L) reduced IK,ACh in a concentration-dependent manner with greater potency in cAF than in SR (−logIC50: 9.1 versus 8.2; P<0.05). Basal current contained a tertiapin-sensitive component that was larger in cAF than in SR (tertiapin [10 nmol/L]-sensitive current at −100 mV: cAF, −6.7±1.2 pA/pF, n=16/5 [myocytes/patients] versus SR, −1.7±0.5 pA/pF, n=24/8), suggesting contribution of constitutively active IK,ACh to basal current. In single-channel recordings, constitutively active IK,ACh was prominent in cAF but not in SR (channel open probability: cAF, 5.4±0.7%, n=19/9 versus SR, 0.1±0.05%, n=16/9; P<0.05). Moreover, IK1 channel open probability was higher in cAF than in SR (13.4±0.4%, n=19/9 versus 11.4±0.7%, n=16/9; P<0.05) without changes in other channel characteristics. Conclusions— Our results demonstrate that larger basal inward rectifier K+ current in cAF consists of increased IK1 activity and constitutively active IK,ACh. Blockade of IK,ACh may represent a new therapeutic target in AF

Ideology and the limits of self-interest: System justification motivation and conservative advantages in mass politics

It is commonly assumed that political attitudes are driven by self-interest and that poor people heavily favor policies aimed at redistributing wealth. This assumption fails to explain the popularity of economic conservatism and the degree of support for the capitalist system. Such outcomes are typically explained by the suggestion that most poor people believe they will become rich one day. In a representative sample of low-income Americans, we observed that less than one-fourth were optimistic about their economic prospects. Those respondents who believed that they would become rich one day were no more likely to endorse the legitimacy of the system and no more supportive of conservative ideology or the Republican Party, compared to those who did not believe they would become rich. From a system justification perspective, we propose that people are motivated to defend the social systems on which they depend, and this confers a psychological advantage to conservative ideology. Providing ideological support for the status quo serves epistemic motives to reduce uncertainty, existential motives to reduce threat, and relational motives to share reality with members of mainstream society. We summarize evidence from the United States, Argentina, Lebanon, and other countries bearing on these propositions—including a survey administered shortly before the 2016 U.S. Presidential election—and discuss political implications of system justification motivation.Fil: Jost, John T.. University of New York; Estados UnidosFil: Langer, Melanie. University of New York; Estados UnidosFil: Badaan, Vivienne. University of New York; Estados UnidosFil: Azevedo, Flávio. Universitat Zu Köln; AlemaniaFil: Etchezahar, Edgardo Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Centro Interdisciplinario de Investigaciones en Psicología Matemática y Experimental Dr. Horacio J. A. Rimoldi; ArgentinaFil: Ungaretti, Joaquín. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Saavedra 15. Centro Interdisciplinario de Investigaciones en Psicología Matemática y Experimental Dr. Horacio J. A. Rimoldi; ArgentinaFil: Hennes, Erin P.. Purdue University; Estados Unido

Nanophotonics for dark materials, filters, and optical magnetism

Research on nanophotonic structures for three application areas is described, a near perfect optical absorber based on a graphene/dielectric stack, an ultraviolet bandpass filter formed with an aluminum/dielectric stack, and structures exhibiting homogenizable magnetic properties at infrared frequencies. The graphene stack can be treated as a effective, homogenized medium that can be designed to reflect little light and absorb an astoundingly high amount per unit thickness, making it an ideal dark material and providing a new avenue for photonic devices based on two-dimensional materials. Another material stack arrangement with thin layers of metal and insulator forms a multi-cavity filter that can effectively act as an ultraviolet filter without the usual sensitivity of the incident angle of the light. This is important in sensing applications where the visible part of the spectrum is to be removed, allowing detection of ultraviolet signals. Finally, achieving a magnetic material that functions at optical frequencies would be of enormous scientific and technological impact, including for imaging, sensing and optical storage applications. The challenge has been to find a guiding principle and a suitable arrangement of constituent materials. A lattice of dielectric spheres is shown to provide a legitimately homogenized material with a magnetic response. This should pave the way for experimental studies. More specifically, a graphene stack is designed, fabricated and characterized. The structure shows strong absorption of light. Spectroscopic ellipsometry is used to obtain the complex sheet conductivity of graphene. Further modeling results establish the graphene stack as the darkest optical material, with lower reflectivity and higher per-unit-length absorption than alternative light-absorbing materials. An optical bandpass filter based on a metal/dielectric structure is modeled, showing performance that is largely independent of the angle of incidence. Parametric evaluations of the reflection phase shift at the metal-dielectric interface provide insight and design information. Filter passbands in the ultraviolet (UV) through visible or longer wavelengths can be achieved by engineering the dielectric thickness and selecting a metal with an appropriate plasma frequency, as demonstrated in simulations. A lattice of suitable dielectric particles is shown to fulfill the requirements for a magnetic optical material. Using Mie theory, the microscopic origin of the magnetic response is explicitly identified as being due to the magnetic dipole resonance of an isolated sphere. This provides a design basis, and dielectric and lattice requirements with candidate dielectrics that will allow magnetic materials to be designed and fabricated for optical applications are presented